A113895 a(n) = C(2+2*n, n) * C(7+2*n, 2+n).

21, 336, 4950, 72072, 1051050, 15402816, 226972746, 3362559200, 50062040028, 748664904000, 11241203533560, 169398104243760, 2561053271692500, 38833447762771200, 590405728218941250, 8998028449224091200, 137437148161776305700, 2103486475191421320000, 32253916565936980114200

Offset: 0

Author

Zerinvary Lajos, Jan 28 2006

Keywords

• easy
• nonn
• changed

Examples

			If n=0 then C(2+2*0,0)*C(7+2*0,2+0) = C(2,0)*C(7,2) = 1*21 = 21.
If n=7 then C(2+2*7,7)*C(7+2*7,2+7) = C(16,7)*C(21,9) = 11440*293930 = 3362559200.
If n=10 then C(2+2*10,10)*C(7+2*10,2+10) = C(22,10)*C(27,12) = 646646*17383860 = 11241203533560.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..830

Crossrefs

Cf. A001791, A002054, A062190.

Programs

Maple

seq(binomial(2+2*n,n)*binomial(7+2*n,2+n), n=0..20); # Robert Israel, Dec 16 2018

Mathematica

nmax = 10; NN[5, m_, x_] := x^m*(2*m+5)!*Hypergeometric2F1[-m, -m, -2*m-5, (x-1)/x]/((m+5)!*m!); tri = Table[CoefficientList[NN[5, m, x], x], {m, 0, 2*nmax+2}]; Table[tri[[2n+3, n+3]], {n, 0, nmax}] (* Jean-François Alcover, Sep 18 2013 *)

PARI

a(n) = binomial(2+2*n,n)*binomial(7+2*n,2+n); \\ Michel Marcus, Sep 18 2013

Formula

a(n) = C(2+2*n, n) * C(7+2*n, 2+n).

From Robert Israel, Dec 16 2018: (Start)

a(n) = A001791(n+1)*A002054(n+3).

24*(11+2*n)*(5+2*n)*(n+3)*a(n+1) - 2*(n+4)*(11*n^2+112*n+252)*a(n+2)+(8+n)*(n+5)*(n+3)*a(n+3) = 0. (End)

a(n) ~ 2^(4*n+9) / (Pi*n). - Amiram Eldar, Sep 06 2025

Extensions

Simpler name and more terms added by Joerg Arndt, Sep 18 2013